Formal Proof of Banach-Tarski Paradox

Daniel de Rauglaudre (1, 2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 PI.R2 - Design, study and implementation of languages for proofs and programs

Banach-Tarski Paradox states that a ball in 3D space is equidecomposable with twice itself, i.e. we can break a ball into a finite number of pieces, and with these pieces, build two balls having the same size as the initial ball. This strange result is actually a Theorem which was proven in 1924 by Stefan Banach and Alfred Tarski using the Axiom of Choice.

Domaines: Logique [math.LO]; Logiciel mathématique [cs.MS]

Daniel de Rauglaudre. Formal Proof of Banach-Tarski Paradox. Journal of Formalized Reasoning, 2017, 10 (1), pp.37-49. ⟨10.6092/issn.1972-5787/6927⟩. ⟨hal-01673378⟩